Meaning of CLOSED in English

2. a: forming a self-contained unit allowing no additions "~ association" b (1): traced by a moving point that returns to an arbitrary starting point "~ curve"; also: so formed that every plane section is a closed curve "~ surface" (2): characterized by mathematical elements that when subjected to an operation produce only elements of the same set "the set of whole numbers is ~ under addition and multiplication" (3): containing all the limit points of every possible subset "a ~ interval contains its endpoints" c: characterized by continuous return and reuse of the working substance "a ~ cooling system" d of a racecourse: having the same starting and finishing point 3 a: confined to a few "~ membership" b: excluding participation of outsiders or witnesses: conducted in strict secrecy c: rigidly excluding outside influence "a ~ mind"